The new Libyan government indicated in December it was prepared to open all files relating to the bombing.

Pan Am flight 103 was blown up over the Scottish town of Lockerbie, killing 270 people.

Bomber Abdelbaset al-Megrahi, a Libyan agent, died last year having been released from a Scottish jail in 2009.

Megrahi was released by the Scottish government on compassionate grounds, suffering from terminal prostate cancer.

He remains the only person ever convicted of the bombing, but Scottish police hope to pursue other suspects in Libya following the country's revolution and downfall of Colonel Gaddafi in 2011.

Abdelbaset al-Megrahi was released from a Scottish prison suffering from cancer

Mr Cameron announced at a joint news conference in Tripoli with his Libyan counterpart Ali Zeidan that officers from Dumfries and Galloway Constabulary had been granted permission to visit the country.

He said: "I am delighted that the Dumfries and Galloway police team will be able to visit your country to look into the issues around the Lockerbie bombing."

The officers are expected to travel to Libya in March.

A spokesman for the police force said: "Dumfries and Galloway Constabulary welcomes the support of the Libyan authorities for the ongoing investigation.

"Travel details and dates cannot be released for security reasons, and to protect the integrity of the investigation."

The father of one of the victims of the bombing welcomed the news but said officers must travel "with an open mind".

Dr Jim Swire, who lost his daughter Flora, believes that Megrahi was wrongly convicted.

Scotland's top prosecutor had previously written to the new Libyan prime minister for help and the UK government had said it was pressing Tripoli "for swift progress and co-operation" on the Lockerbie case.

In April last year, Scotland's Lord Advocate Frank Mulholland travelled to Tripoli with the director of the FBI, Robert Mueller, requesting co-operation after the fall of Gaddafi.

This was followed in May by a meeting with Libya's interim prime minister in London to discuss further inquires into the bombing.

A statement from the Crown Office in Scotland said it welcomed Libyan support for the ongoing investigation.

A Crown Office spokesperson said: "The investigation into the involvement of others with Megrahi in the Lockerbie bombing remains open and Dumfries and Galloway Constabulary continues to work with Crown Office and US authorities to pursue available lines of enquiry."